

where \(T_{\mu \nu }=-\frac{2}{\sqrt{-g}}\frac{\delta S_{\text{matter}}}{\delta g^{\mu \nu }}\) 
denotes the source matter stress-energy tensor and \(\Box =g^{\mu \nu }\nabla _\mu \nabla _\nu \) . Remarkably, their solutions can be transform from one frame to another by making use of metric conformal transformation and scalar field redefinition. Thus the totality of all frames can be divided into solution equivalent classes As discussed many times in the literature, see e.g. [1]} - [2]}, solution or mathematically equivalent frames are not physically equivalent..
